Dynamic Stability of Super-Elliptical Plates Resting on Elastic Foundations under Periodic In-Plane Loads

• Published in: Journal of engineering mechanics
• Main Authors: Hasheminejad, Seyyed M, Keshvari, M M, Ashory, M R
• Format: Journal Article
• Language: English
• Published: 19.03.2013
• Subjects: Dynamic stability; Foundations; Loads (forces); Mathematical analysis; Mathematical models; Panels; Parameters; Plates
• ISSN: 0733-9399
• DOI: 10.1061/(ASCE)EM.1943-7889.0000630

Dynamic instability of thin clamped flat isotropic elastic panels of super-elliptical planform set on a two parameter Winkler-Pasternak foundation, and subjected to uniformly distributed pulsating inplane loads, is theoretically investigated. The plate perimeter is described by a super-elliptic function with a power, corresponding to shapes ranging from a circle (ellipse) to a square (rectangle). The classical Galerkin procedure is utilized to reduce the problem into a set of non-dimensional coupled Mathieu-Hill equations, and the regions of parametric instability for principal and combination resonant frequencies are determined by applying Hsu's technique. The effects of the super-ellipticity parameter, plate aspect ratio, and foundation stiffness on the dynamic stability behavior (onset and width of the instability regions) are examined. Moreover, the transient flexural response of the panel under an static in-plane load and subjected to a transverse uniform step force is obtained. The validity of results is established by comparison with the available data as well as with the aid of a commercial finite element package. The proposed model is believed to be the first rigorous attempt for dynamic stability and/or flexural dynamic response analysis of super-elliptical plates.